The different geometric position of left and right eye leads to small differences between the images on the two retinae. The disparity of the images is used by the visual system to infer depth. A central challenge consists in identifying corresponding features in the two eyes called the stereo correspondence problem. Visual neurons suffer from the problem that responses to non-corresponding images (false matches) can be as large as those to correct matches. The disparity-energy model has been widely used to explain the disparity tuning of neurons in the primary visual cortex (V1). This model passes the image through linear filters in each eye, and then passes the binocular sum through an output nonlinearity. It is a member of a widely used class of linear-nonlinear (LN) models. The original disparity-energy model placed strong constraints on the linear filters: there were exactly two parallel elements (a quadrature pair), both of which are excitatory. Both elements used the same rule (e.g. a simple translation) to apply a disparity between left and right eye filters a receptive field (RF) disparity. These two elements elegantly capture many properties of disparity selective neurons. However, such a simple model is inevitably an approximation understanding how real neurons deviate from this approximation has helped clarify how they compute disparity. The energy model responds best (on average) to stimuli with a disparity that matches the RF disparity. Nonetheless (as with many other detectors), in any one image, stronger activation may be produced by a disparity that does not match. This means that the particular image projected on one models RFs might lead to a stronger response in another model neuron with a different RF disparity. It is therefore unclear how the correct depth can be inferred from a population of such neurons. Work performed under this project in previous years has suggested that responses to false matches may be attenuated by adding elements to the original model. In order to characterize these putative elements with as few assumptions as possible, we analyzed the spiking responses of neurons in the primate V1 with a spike-triggered covariance approach. This revealed that neuronal responses are characterized by a combination of both excitatory and inhibitory elements. Furthermore, the elements'filters are arranged in a way that results in a suppression of neuronal responses to false matches. We showed that this combination of excitatory and suppressive elements helps to reduce the problem of false matches in the stereo correspondence problem.